A few things.
RLB is a faction leader in the way that LRM is not. I had never heard of LRM before this week.
I do think that overall Starmer is making a statement of intent whilst trying to avoid all out factional war within the Labour Party.
I also think he is well aware of where public opinion on both antisemitism and trans issues lie with the public.
He has to be seen to push back on antisemitism more than the trans issue because of where public awareness on the matter was. Corbyn was very much framed as the antisemitic leader and for Starmer to break from the past and forge a new political identity for both himself and the Labour Party he has to come down hard on it, especially when it comes to high profile Corbyn allies / Corbyn front benchers.
His position on women isn't quite as pronounced. Labour have a problem with winning over male voters: women are already much more likely to support Labour. He has more room to move here.
And he has pushed back whether or not we think it's not. He's said that we need a debate on this subject and that it's nuanced. That's different from Corbyn.
For various reasons (some of which I've put on another thread) I think this is a long game and pushback from any political party will be a long game.
For now, it will be framed that Starmer is being sexist. I personally think that this may be the case but I also think that there are limits as to how much he can do all at once too.